The most sensitive assay for antibodies is the solid phase radioimmunoassay in which picomolar quantities of antibody can be accurately detected by binding to antigens attached to a solid phase. It would be highly desirable to obtain from such assays the intrinsic affinities of the antibody for the antigen, the size of the antibody, and its valency. Previous theoretical approaches to this problem have assumed that the lattices are "dilute" containing at most two antigens. However, the antigens may be closely packed so that excluded volume effects, where adjacent lattice sites are blocked, become important to the binding. The fact that each antibody is multivalent, i.e., can bind to more than one antigen, further complicates the overall process. Thus, any theory of antibody binding to antigen lattices should include the effects of many antigen sites, the effects of excluded volume and the multivalency of the antibody.